I'm not sure why we are even arguing here, you can go into Codex or ChatGPT Work and start using 5.6. It'll start draining your weekly Codex limit. There's no unlimited 5.6 in Codex.
I'm just going by what I see on the linked page. Under the Pro section ($100+) it says unlimited 5.6, and Codex usage is included in all tiers. So I can only conclude that unlimited 5.6 is available in Codex (for $100+/month). If that isn't the case then may want to contact support.